논문KCI 등재
ON DECOMPOSITIONS OF THE COMPLETE EQUIPARTITE GRAPHS Kkm(2t) INTO GREGARIOUS m-CYCLES
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초록
For an even integer m at least 4 and any positive integer t, it is shown that the complete equipartite graph Kkm(2t) can be decomposed into edge-disjoint gregarious m-cycles for any positive integer k under the condition satisfying (m-1)2+34m < k. Here it will be called a gregarious cycle if the cycle has at most one vertex from each partite set.
Abstract
For an even integer m at least 4 and any positive integer t, it is shown that the complete equipartite graph Kkm(2t) can be decomposed into edge-disjoint gregarious m-cycles for any positive integer k under the condition satisfying (m-1)2+34m < k. Here it will be called a gregarious cycle if the cycle has at most one vertex from each partite set.
참고문헌 (13)
- B. Alspach, "Cycle decompositions of Kn and KnI", J. Combin. Theory Ser. B, 81, pp.77~99 (2001)
- E. Billington, "Decomposition of complete tripartite graphs into gre- garious 4-cycles", Discrete Math, 261, pp.87~111 (2003)
- E. Billington, "Equipartite and almost-equipartite gregarious 4-cycle systems", Discrete Math, 308, pp.696~714 (2008)
- E. Billington, "Resolvable gregarious cycle decompo- sitions of complete equipartite graphs", Discrete Math, 308, pp.2844~2853 (2008)
- E. Billington, "Equipartite gregarious 6- and 8-cycle systems", Discrete Math, 307, pp.1659~1667 (2007)
- N. J. Cavenagh, "Decompositions of complete multipartite graphs into cycles of even length", Graphs and Combinatorics, 16, pp.49~65 (2000)
- 조정래, "A note on decomposition of complete equipartite graphs into gregarious $6$-cycles", 대한수학회보, 44(4), pp.709~719 (2007), 대한수학회
- J. R. Cho, "A difference set method for cir- cular decompositions of complete mutipartite graphs into gregarious 4-cycles", Preprint, ~
- 조정래, "DECOMPOSITIONS OF COMPLETE MULTIPARTITE GRAPHS INTO GREGARIOUS 6-CYCLES USING COMPLETE DIFFERENCES", 대한수학회지, 45(6), pp.1623~1634 (2008), 대한수학회
- J. R. Cho, "Decompositions of Kkm+1(2t) into Gregarious m-cycles using Di erence Sets", Preprint, ~
- M. Sajna, "On decomposiing Kn I into cycles of a xed odd length", Descrete Math, 244, pp.435~444 (2002)
- M. Sajna, "Cycle decompositions III: complete graphs and fixed length cycles", J. Combin. Designs, 10, pp.27~78 (2002)
- Benjamin R., "Smith, Some gregarious cycle decompositions of complete equipartite graph", E. J. of Combinatorics, 16(1), pp.R135~ (2009)
관련 논문AI추천
Circulant Decompositions of Certain Multipartite Graphs into Gregarious Cycles of a Given Length조정래영남수학회 · East Asian Mathematical Journal2014 · 제30권 제3호A REMARK ON CIRCULANT DECOMPOSITIONS OF COMPLETE MULTIPARTITE GRAPHS BY GREGARIOUS CYCLES조정래영남수학회 · East Asian Mathematical Journal2017 · 제33권 제1호A note on decomposition of complete equipartite graphs into gregarious $6$-cycles조정래대한수학회 · 대한수학회보2007 · 제44권 제4호DECOMPOSITIONS OF COMPLETE MULTIPARTITE GRAPHS INTO GREGARIOUS 6-CYCLES USING COMPLETE DIFFERENCES조정래, Ronald J. Gould대한수학회 · 대한수학회지2008 · 제45권 제6호A difference set method for circulant decompositions of complete partite graphs into gregarious 4-cycles김은경, 조영민, 조정래영남수학회 · East Asian Mathematical Journal2010 · 제26권 제5호DISJOINT CYCLES WITH PRESCRIBED LENGTHS AND INDEPENDENT EDGES IN GRAPHSHong Wang대한수학회 · 대한수학회지2014 · 제51권 제5호
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